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Math  /  Trigonometry

QuestionIf the adjacent side of a triangle is 56.7 units long, and the hypotenuse is 71.2 units long, what is the length of the side opposite? (A) 41.23 units (B) 43.02 units (C) 43.06 units (D) 42.27 units

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The adjacent side and hypotenuse are given.
3. We are to find the length of the side opposite.

STEP 2

1. Recall the Pythagorean theorem.
2. Substitute the given values.
3. Solve for the length of the opposite side.
4. Compare the calculated length with the given options.

STEP 3

Recall the Pythagorean theorem, which relates the sides of a right triangle:
c2=a2+b2 c^2 = a^2 + b^2
where c c is the hypotenuse, a a is the adjacent side, and b b is the opposite side.

STEP 4

Substitute the given values into the Pythagorean theorem:
71.22=56.72+b2 71.2^2 = 56.7^2 + b^2

STEP 5

Solve for b2 b^2 :
b2=71.22−56.72 b^2 = 71.2^2 - 56.7^2
Calculate 71.22 71.2^2 and 56.72 56.7^2 :
71.22=5069.44 71.2^2 = 5069.44 56.72=3213.69 56.7^2 = 3213.69
Now substitute back:
b2=5069.44−3213.69 b^2 = 5069.44 - 3213.69 b2=1855.75 b^2 = 1855.75
Take the square root to find b b :
b=1855.75 b = \sqrt{1855.75} b≈43.06 b \approx 43.06

STEP 6

Compare the calculated length with the given options:
The calculated length is approximately 43.06 43.06 units, which matches option (C).
The length of the side opposite is:
43.06 units \boxed{43.06 \text{ units}}

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